Dead reckoning - Appropedia: The sustainability wiki Appropedia needs your support - Please Donate Today Dead reckoning Jump to: navigation , search Dead reckoning (DR) is the process of estimating one's current position based upon a previously determined position, or fix, and advancing that position based upon known or estimated speeds over elapsed time, and course. Contents 5 External links Workings and requirements[ edit ] In practice dead reckoning works by noting down your current position regularly by taking into account your previous position and determining where you are now having used a certain compass coarse. You are able to determine where you are now since you know the time that has elapsed since your last position the speed by which you were travelling and any events that changed your direction of travel (ie wind, currents, ...) So before being able to use dead reckoning it is vital that you have pencil, and a map of the area on which meridians and parallells are marked. For reasons of accuracy, you need a detailed map and have the parallells marked per 5 minutes (5') you know the variation in the area in which you are travelling you have a compass, accurate watch, and (preferably) instruments to record strength of the wind, currents, ...

have recorded the time of travelling, ... in a (ship's) log Compensating for compass incorrection, drift (wind) and drift (current)[ edit ] File:Plotting a course.JPG Plotting a coarse When plotting a course, there are 2 incorrections associated with the use of the compass that need to be corrected. Also, the drift from wind and current needs to be compensated. Formula: Compass course + magnetic deviation + magnetic variation + drift (wind) + drift (current) = Course over water (or ship track) Note: Compass course + magnetic deviation + magnetic variation = True course Note: Compass course + magnetic deviation + magnetic variation + drift (wind) = Course over ground (or airship track) Magnetic deviation[ edit ] Compass deviation table The magnetic deviation is the incorrection which occurs due to the presence of metal parts/objects on the ship. On wooden (or plastic) vessels it is nonexistent. On metal ships, a compass deviation table (see right image) needs to be present. The deviation varies depending on the heading. Magnetic variation[ edit ] The magnetic variation is an icorrection caused by the earth itself; it varies depending on the location and the year. The variation can be either west or east.

If the variation is west, it means that the magnetic north is west of the true north. It then receives a - sign. If the variation is east, it means that the magnetic north is east of the true north. It then receives a + sign. Note: on most (nautical) maps, the variation is often shown for the particular location of the map on a compass rose (solely for the year of purchase of the map) Measuring distance on your (paper) map[ edit ] Given that the circumferenece of a meridian is exactly 40 000 km; 1 minute on the meridian (1') is exactly 1,852 km. One degree is 111,12 km [1] . The minutes/degrees of the parallels can't be used (since the parallells differ in size; ie the 0° parallell is much longer than those more towards the north or south pole. The required length can be simply taken over from the meridian using a thumbscrew compass and used to draw out the course/track.

Given that 1,852km is exactly the length of 1 nautical mile (knot), it facilitates things as well; we can simply extent the measured distance by the amount of hours we travelled at a given amount of knots/h. Drift (wind) and drift(current)[ edit ] The amount of drift will differ depending on the strength/exact heading; however a counteracting of 5° (in the opposite direction) is often taken as a baseline for drift (wind) and 10° for drift (current) when any drift is encountered. Taking a bearing now and then[ edit ] A significant disadvantage of dead reckoning is that since new positions are calculated solely from previous positions, the errors of the process are cumulative, so the error in the position fix grows with time . To counteract this, it is important to take a bearing once and a while to ensure that the positions you calculated are still correct. The taking of a bearing can be done using a sextant or GPS/Galileo receiver.

Also, using a map, we can also take a bearing "on sight"; ie by cross checking specific points of intrest (ie buoys, depth of the sea, church, ...) on the map and your current position you can often determine whether your position is still accurate. The checking of the depth of the sea can be done by means of a sounding line . Dead reckoning - Wikipedia, the free encyclopedia Dead reckoning For other uses, see Dead reckoning (disambiguation) . The navigator plots his 9am position, indicated by the triangle, and, using his course and speed, estimates his position at 9:30am and 10am. Dead reckoning (DR) is the process of estimating one's current position based upon a previously determined position, or fix , and advancing that position based upon known or estimated speeds over elapsed time, and course. While traditional methods of dead reckoning are no longer considered primary in most applications, modern inertial navigation systems , which also depend upon dead reckoning, are very widely used.

Contents [ edit ] Animal navigation In studies of animal navigation, dead reckoning is more commonly (though not exclusively) known as path integration , and animals use it to estimate their current location based on the movements they made since their last known location. Animals such as ants, rodents, and geese have also been shown to continuously keep track of their locations relative to a starting point and return to it, an important skill to have for creatures that forage for food and then return to a fixed home. [1] [ edit ] Marine navigation In marine navigation a "dead" reckoning plot generally does not take into account the effect of currents or wind . Aboard ship a dead reckoning plot is considered important in evaluating position information and planning the movement of the vessel. [2] Dead reckoning begins with a known position, or fix , which is then advanced, mathematically or directly on the chart, by means of recorded heading, speed, and time. Speed can be determined by many methods. Before modern instrumentation, it was determined aboard ship using a chip log . More modern methods include pit log referencing engine speed (e.g.

in rpm ) against a table of total displacement (for ships) or referencing one's indicated airspeed fed by the pressure from a Pitot tube . This measurement is converted to an equivalent airspeed based upon known atmospheric conditions and measured errors in the indicated airspeed system. A naval vessel uses a device called a pit sword (rodmeter), which uses two sensors on a metal rod to measure the electromagnetic variance caused by the ship moving through water. This change is then converted to ship's speed. Distance is determined by multiplying the speed and the time. This initial position can then be adjusted resulting in an estimated position by taking into account the current (known as set and drift in marine navigation). If there is no positional information available, a new dead reckoning plot may start from an estimated position. In this case subsequent dead reckoning positions will have taken into account estimated set and drift. Dead reckoning positions are calculated at predetermined intervals, and are maintained between fixes. The duration of the interval varies. Factors including one's speed made good and the nature of heading and other course changes, and the navigator's judgment determine when dead reckoning positions are calculated.

Before the development of the marine chronometer , dead reckoning was the primary method of determining longitude available to mariners such as Christopher Columbus and John Cabot on their trans-Atlantic voyages. [ edit ] Air navigation Traditionally, in air navigation , displacement or position caused by wind were taken into account, using a tool called a wind triangle . Generally speaking, dead reckoning positions were calculated at least once every 300 miles and when making combined turns totaling more than 30 degrees from the initial heading out of the last DR position. Today, dead reckoning is rarely used in this traditional form for air navigation, but it survives in the form of inertial navigation systems , which are nearly universal on more advanced aircraft. The INS is used in combination with other navigation aids, such as GPS , in order to provide reliable navigation capability under virtually any conditions, with or without external navigation references. [ edit ] Ground Transportation Prior to the advent of GPS Technology some public transportation systems used dead reckoning to track their fleets. Transponders placed along the service routes would act as the fixed points. Transponders would be installed at major intersections and hydro poles along the routes enabling the management to monitor operations from a central location and make service adjustments based on the data.

A major downside to this technology for the purpose of Ground Transportation is that if a bus goes off route for any reason (diversion for an accident, roadwork, etc.) the Vehicle would simply appear to be held at its last known position or drop off the tracking map all together. The Toronto Transit Commission still uses this technology for its streetcar and bus fleets, however has indicated that they soon plan on implementing GPS on all their surface vehicles. [3] [ edit ] Etymology There is disagreement about the derivation of the phrase. It is popularly thought to come from deduced reckoning and is sometimes given in modern sources as an alternatively spelled ded reckoning; however, according to the Oxford English Dictionary , the phrase dead reckoning dates from Elizabethan times (1605–1615). The popular etymology from deduced is not documented in the Oxford English Dictionary or any other historical dictionary. Dead reckoning is navigation without stellar observation. With stellar observation, you are "live," working with the stars and the movement of the planet.

With logs, compasses, clocks, but no sky, you are working "dead." In an extended discussion on "dead vs "ded", the Straight Dope Science Advisory Board summarises it as follows: The term dates from the seventeenth century, so we have to look to the sea for the origin of the term, not the air. One theory is that dead reckoning was first called "deduced reckoning," which someone then abbreviated (in a ship's log) as "ded. reckoning." Later someone reading it thought "ded" didn't make much sense, so he wrongly (according to this theory) thought it must be a misspelling for "dead." The other theory is that it was "dead reckoning" from the beginning, but since this sort of navigation doesn't seem to have much to do with death, someone assumed the derivation from "deduced," which must have made more sense to him. In either case, folk etymology is at work, but it isn't immediately obvious which is the real etymology and which is the folk etymology. There is an extended bibliography and encyclopedic references accompanying the above article.

Video: Cross country deviations on the fly – MzeroA.com Learn how to perform your cross country deviations like a pro Jeremy Hello Jason, Great video – however I disagree with your definition of dead reckoning. Dead reckoning is properly defined as “the process of estimating one’s current position based upon a previously determined position, or fix, and advancing that position based upon known or estimated speeds over elapsed time, and course.” (Wikipedia) To keep your navigation accurate, of course, you establish a new fix from time to time. You can do this with a visual reference, or with radio navigation aids – the method you use to establish the fix is unimportant in the definition and practice of dead reckoning. Your ‘wind card’ method is part of using dead reckoning navigation to carry out the deviation – notice this doesn’t involve radios or visual references at all, unless you wanted to establish a new fix. That’s the whole point – and one possible reason it’s called “dead” – is because it’s done solely by math… until the new fix is established by whatever means. Some more references: Jeremy Wayne Conrad Good video, thanks!

I’ve never heard of dead reckoning defined as “the use of navigational equipment to pinpoint your location,” though. Dead reckoning means you start from a known location, and from there it’s your estimated ground speed, your estimated track over the ground, and your trusty stopwatch that gives you an estimate for where you are. Pilotage is one way to know where you have actually gone, as opposed to where dead reckoning estimates you have gone. The use of a VOR or GPS receiver is another way. To see if someone truly understands navigation and flying, ask them: if they could have only one instrument in the airplane, what would it be? I think the answer ought to be “the magnetic compass.” Allow them one more instrument and maybe it should be “A clock or stopwatch.” With those two simple, nearly foolproof instruments, you can navigate anywhere in the VFR skies. The rest of your flight information you can get from other sources (airspeed from control feel and slipstream noise. Altitude, approximately, by looking outside. Attitude by looking outside. And so on.) Academically speaking, of course, since all prudent pilots fly with the instruments required by the FARs.

PS: Not a pilot, so all of the above might be utter nonsense. Consult someone who knows something instead of me. Wayne Conrad Good video, thanks! I’ve never heard of dead reckoning defined as “the use of navigational equipment to pinpoint your location,” though. Dead reckoning means you start from a known location, and from there it’s your estimated ground speed, your estimated track over the ground, and your trusty stopwatch that gives you an estimate for where you are. Pilotage is one way to know where you have actually gone, as opposed to where dead reckoning estimates you have gone. The use of a VOR or GPS receiver is another way. To see if someone truly understands navigation and flying, ask them: if they could have only one instrument in the airplane, what would it be? I think the answer ought to be “the magnetic compass.” Allow them one more instrument and maybe it should be “A clock or stopwatch.” With those two simple, nearly foolproof instruments, you can navigate anywhere in the VFR skies. The rest of your flight information you can get from other sources (airspeed from control feel and slipstream noise. Altitude, approximately, by looking outside. Attitude by looking outside.

And so on.) Academically speaking, of course, since all prudent pilots fly with the instruments required by the FARs. PS: Not a pilot, so all of the above might be utter nonsense. Consult someone who knows something instead of me. Wayne Conrad Good video, thanks! I’ve never heard of dead reckoning defined as “the use of navigational equipment to pinpoint your location,” though. Dead reckoning means you start from a known location, and from there it’s your estimated ground speed, your estimated track over the ground, and your trusty stopwatch that gives you an estimate for where you are. Pilotage is one way to know where you have actually gone, as opposed to where dead reckoning estimates you have gone. The use of a VOR or GPS receiver is another way. To see if someone truly understands navigation and flying, ask them: if they could have only one instrument in the airplane, what would it be? I think the answer ought to be “the magnetic compass.” Allow them one more instrument and maybe it should be “A clock or stopwatch.” With those two simple, nearly foolproof instruments, you can navigate anywhere in the VFR skies.

The rest of your flight information you can get from other sources (airspeed from control feel and slipstream noise. Altitude, approximately, by looking outside. Attitude by looking outside. And so on.) Academically speaking, of course, since all prudent pilots fly with the instruments required by the FARs. PS: Not a pilot, so all of the above might be utter nonsense. Consult someone who knows something instead of me. Wayne Conrad Good video, thanks! I’ve never heard of dead reckoning defined as “the use of navigational equipment to pinpoint your location,” though. Dead reckoning means you start from a known location, and from there it’s your estimated ground speed, your estimated track over the ground, and your trusty stopwatch that gives you an estimate for where you are. Pilotage is one way to know where you have actually gone, as opposed to where dead reckoning estimates you have gone. The use of a VOR or GPS receiver is another way. To see if someone truly understands navigation and flying, ask them: if they could have only one instrument in the airplane, what would it be?

I think the answer ought to be “the magnetic compass.” Allow them one more instrument and maybe it should be “A clock or stopwatch.” With those two simple, nearly foolproof instruments, you can navigate anywhere in the VFR skies. The rest of your flight information you can get from other sources (airspeed from control feel and slipstream noise. Altitude, approximately, by looking outside. Attitude by looking outside. And so on.) Academically speaking, of course, since all prudent pilots fly with the instruments required by the FARs. PS: Not a pilot, so all of the above might be utter nonsense. Consult someone who knows something instead of me. Search for: Dead reckoning : Wikis (The Full Wiki) The Full Wiki More info on Dead reckoning Wikis Advertisements Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles . Related top topics For other uses, see Dead reckoning (disambiguation) .

The navigator plots his 9am position, indicated by the triangle, and, using his course and speed, estimates his position at 9:30am and 10am. Dead reckoning (DR) is the process of estimating one's current position based upon a previously determined position, or fix , and advancing that position based upon known or estimated speeds over elapsed time, and course. While traditional methods of dead reckoning are no longer considered primary means of navigation , modern inertial navigation systems , which also depend upon dead reckoning, are very widely used. A disadvantage of dead reckoning is that since new positions are calculated solely from previous positions, the errors of the process are cumulative, so the error in the position fix grows with time. Contents 10 External links Animal navigation In studies of animal navigation, dead reckoning is more commonly (though not exclusively) known as path integration , and animals use it to estimate their current location based on the movements they made since their last known location. Animals such as ants, rodents, and geese have also been shown to continuously keep track of their locations relative to a starting point and return to it, an important skill to have for creatures that forage for food and then return to a fixed home.

Marine navigation In marine navigation a "dead" reckoning plot generally does not take into account the effect of currents or wind . Aboard ship a dead reckoning plot is considered important in evaluating position information and planning the movement of the vessel. [1] Dead reckoning begins with a known position, or fix , which is then advanced, mathematically or directly on the chart, by means of recorded heading, speed, and time. Speed can be determined by many methods. Before modern instrumentation, it was determined aboard ship using a chip log . More modern methods include pit log referencing engine speed (e.g. in rpm ) against a table of total displacement (for ships) or referencing one's indicated airspeed fed by the pressure from a Pitot tube . This measurement is converted to an equivalent airspeed based upon known atmospheric conditions and measured errors in the indicated airspeed system. A naval vessel uses a device called a pit sword (rodmeter), which uses two sensors on a metal rod to measure the electromagnetic variance caused by the ship moving through water. This change is then converted to ship's speed. Distance is determined by multiplying the speed and the time.

This initial position can then be adjusted resulting in an estimated position by taking into account the current (known as set and drift in marine navigation). If there is no positional information available, a new dead reckoning plot may start from an estimated position. In this case subsequent dead reckoning positions will have taken into account estimated set and drift. Dead reckoning positions are calculated at predetermined intervals, and are maintained between fixes. The duration of the interval varies. Factors including one's speed made good and the nature of heading and other course changes, and the navigator's judgment determine when dead reckoning positions are calculated. Before the development of the marine chronometer , dead reckoning was the primary method of determining longitude available to mariners such as Christopher Columbus and John Cabot on their trans-Atlantic voyages. Tools such as the Traverse board were developed to enable even illiterate crew members collect the data needed for dead reckoning. Air navigation Traditionally, in air navigation , displacement or position caused by wind were taken into account, using a tool called a wind triangle . Generally speaking, dead reckoning positions were calculated at least once every 300 miles and when making combined turns totaling more than 30 degrees from the initial heading out of the last DR position.

Today, dead reckoning is rarely used in this traditional form for air navigation, but it survives in the form of inertial navigation systems , which are nearly universal on more advanced aircraft. The INS is used in combination with other navigation aids, such as GPS , in order to provide reliable navigation capability under virtually any conditions, with or without external navigation references. Automotive navigation Dead reckoning is today implemented in some high-end automotive navigation systems in order to overcome the limitations of GNSS technology alone. Satellite microwave signals are unavailable in parking garages and tunnels , and often severely degraded in urban canyons and near trees due to blocked lines of sight to the satellites or multipath propagation . In a dead-reckoning navigation system, the car is equipped with sensors that record the wheel rotation and steering direction. These sensors are often already present in cars for other purposes ( anti-lock braking system , electronic stability control ) and can be read by the navigation system from the controller-area network bus. The navigation system then uses a Kalman filter in order to integrate the reliability and short-term accuracy of the sensor data with the long-term accuracy of the satellite data into a position fix that combines the best of both worlds. Etymology There is disagreement about the derivation of the phrase.

It is sometimes thought (particularly among sailors and pilots in the USA [2] ) to come from deduced reckoning and is sometimes given in modern sources as an alternatively spelled ded reckoning. According to the Oxford English Dictionary , the phrase dead reckoning dates from Elizabethan times (1605–1615). [3] The popular etymology from deduced is not documented in the OED or any other historical dictionary. It is not clear what 'dead' might mean in the context of dead reckoning, and several alternative theories have been promulgated.

[2] Dead reckoning in literature In Walden, Henry David Thoreau suggests the following approach to life: "In the midst of this chopping sea of civilized life, such are the clouds and storms and quicksands and thousand-and-one items to be allowed for, that a man has to live, if he would not founder and go to the bottom and not make his port at all, by dead reckoning, and he must be a great calculator indeed who succeeds." In "Moby Dick, or, The Whale" Herman Melville states on page 507: "...and in these same perilous seas, gropes he not his way by mere dead reckoning of the error-abounding log?" Differential drive dead reckoning Here are the dead reckoning formulas for the coordinates (x and y), and heading (θ) for a differential drive robot with encoders on both drives: Δx = RWcos(θ)(T1 + T2) Δy = RWsin(θ)(T1 + T2) where T1 are the encoder ticks recorded on drive one, T2 are the encoder ticks recorded on drive two, RW is the radius of each drive wheel, and TR is the number of encoder ticks recorded in a full,

 in-place rotation.

See also Assignment 1: Puget Sound Geography Tudor Navigation and Seamanship by Peter Whitlock Navigational science of the period was a rather hit or miss affair, particularly out of sight of land, and was basically to remain so until the mid 18th century. The tools of the pilot or navigator in Tudor Tudor refers to the period in England from 1485-1603 during the reigns of Henry VII, Henry VIII, and Elizabeth I. times were relatively crude. The spyglass, later to be called the telescope, did not evolve until the early part of the 17th century, and a means of scientifically anticipating the weath er was not available until the arrival of the barometer in 1643. No adequate survey of the British coastline existed until the end of the 16th century. Nevertheless, the 16th century saw tremendous advances in the science of navigation. Seamen had evolved rule of thumb methods of using the sun, stars and moon for direction finding since time out of mind, but now the scholar and the pilot were to work in unison in Portugal.

The pilot was taught to use instruments and it is interesting to note that Sir Francis Drake used Portuguese pilots - Late in 1577, Francis Drake left England with five ships. On reaching Africa, the true destination was revealed to be the Pacific Ocean via the Strait of Magellan. Still in the eastern Atlantic, a Portuguese merchant ship and its pilot were captured and the pilot was to stay with Drake for 15 months. Sir Francis Drake, an English Admiral, acquired the Portuguese navigational skills for England.Portuguese pilots. was the lead and line , essential for letting the pilot know the water depth, and at the same time, the nature of the seabed. This latter information was useful in helping them to identify the section of coast, the distance off shore and for locating suitable holding ground to anchor in. This was achieved by sticking a pice of tallow in the bottom of the lead, allowing sand, shingle and shells to adhere to it. One of the basic items of navigation was the lead and line , essential for letting the pilot know the water depth, and at the same time, the nature of the seabed.

This latter information was useful in helping them to identify the section of coast, the distance off shore and for locating suitable holding ground to anchor in. This was achieved by sticking a piece of tallow (Suet fat) in the bottom of the lead, allowing sand, shingle and shells to adhere to it. The lead weighed 7lbs or 14lbs, with 28lbs for a deep-sea lead, weights that are still the same. The line was marked with pieces of cloth, rope and leather at certain fathom marks so that the leadsman could identify the nearest mark by sight during the day and by feel at night. The "Log" (or sounding-lead) was used to measure the speed of a ship through the water. A piece of wood with a "stray" line attached was thrown off the stern of the ship until it floated clear. This stray line was in turn attached to a rope reeled on a hand held drum. As the ship moved away from the floating log the reel turned and the rope was allowed to run off for a specified period of time measured by a sand glass.

The line was marked by knots in the rope at proportionate distances and at the end of the specified period the number of knots to run off the reel was recorded. This gave rise to the term "knots" to express nautical miles per hour. The "league" was the common usage for expressing distances in Tudor times. Finding the ship's position when in sight of land wasn't too difficult, except when exploring uncharted waters. Pilots became familiar with land marks, water colour, scend of the sea, tidal stream lore, even the smell of a certain area. This led to the sensible policy of employing pilots for a specific area, as with Trinity House pilots today. It is noteworthy that the Trinity House for the Advancement of Navigation and Training in Pilotage was formed by Henry VIII in 1514. Thomas Spert, Master of the Mary Rose Mary Rose was a warship of the English Tudor navy of King Henry VIII.in 1513, was appointed master of Trinity House at its inception. The pilot was directly concerned with the science of astronomy, he needed to know the "age" and bearing of the moon for the purpose of tidal prediction.

Tide tables were already in being, although the true cause of tides was not yet understood. The measurement of North - South movement (latitude) and East - West movement (longitude) presented another set of problems. Latitude was measured by taking a "sight" of the altitude of a heavenly body, usually the altitude of the midday sun, or a star, primarily the Pole Star in Northern latitudes. The instrument used for this purpose in the period of the Mary Rose would have been either an astrolabe or more likely, a cross staff . In conjunction with astronomical tables published in Lisbon in 1509, the latitude of a ship could be reasonably accurately determined. Longitude was another matter entirely. At the time of the Mary Rose this was achieved by "dead reckoning - is the process of estimating one's current position based upon a previously determined position, or fix, and advancing that position based upon known or estimated speeds over elapsed time, and course.Dead reckoning (DR)", a form of guesstimate of distance and direction over a given time. The log and sand glass combination gave the speed of the ship, with the course being obtained from the compass.

This information was plotted on the " traverse board ", a form of peg board on a compass rose . Pegs were inserted every half hour of a four hour watch to show course and estimated distance covered. This information would be interpreted by the pilot and transferred to his " portolan chart " using his dividers for the plotting. The pilot could now estimate his east - west distance travelled to give him longitude. His cross staff would give him a latitude check. So far no traverse board or cross staff have been identified on the Mary Rose. There were of course considerable errors, the roll of the ship could impede the flow of sand in the glass and bad weather could make sun or star sights impossible for days on end. The measurement of time was assisted by the use of pocket sundials. These gave the local time by the sun at the particular latitude they were set for. Nine pocket sundials were found aboard the Mary Rose. The sun dials ' built in compass needle enabled them to be orientated to magnetic north. Really accurate measurement of longitude had to wait for the development of a reliable ship born clock, the Harrison Chronometer of the 1770s finally allowed navigators to do so.

The chart had existed since the middle of the thirteenth century. These were called "portolans" and probably originated in Venice or Genoa. This sheep or goatskin chart gave coastal outlines with the positions of ports marked on them. Compass roses featured all over these charts to enable courses to be plotted. By the 16th century, these charts were in common use by the Portuguese. The existence of dividers on the Mary Rose may indicate that the ship carried charts. The pilots of the period also had a "portolano", a form of sailing directions that went with such charts. This described coasts and ports, anchorages, rocks, etc. The successor to the portolano, the routier routier - from French routier and Dutch ruiter, meaning "something that finds a way". Rutter is a coastal map showing town names and pictures of landmark buildings (church steeples, forts, prominent landforms, etc.) that could be recognized from a passing ship. or " rutter ," was becoming popular in the 16th century. These followed the format of present day sailing directions, giving tidal information and views of the coast as seen from seaward.

In 1541, "The New Rutter of the Seas for North Partes" was published for circumnavigation of the British Isles. By the 16th century the compass was becoming an essential aid for the navigator. The compasses on the Mary Rose were mounted on gimbals in a bowl to compensate for the movement of the ship. The compass bowls had glass tops and were set in wooden boxes for protection. The pilot also needed a lodestone , a piece of magnetic oxide of iron. (The Pole Star was often referred to as "The Lodestar"). This stone was used to stroke, and thereby magnetise, the compass needle. The compass needle points not to true north, but to magnetic north, a wandering point in the Canadian Arctic. The angular difference between true north and magnetic north on any part of the earth's surface is known as "variation". By 1530, the Portugese had the means of measuring and tabulating variation. Another error of the compass is caused iron fitting and items within the ship. This causes a deflection of the needle known as "deviation". ©2011, Robert E. Lee. All rights reserved.

No part of this publication may be reproduced in any form or by any means without permission in writing from the publisher. Dead reckoning - GIS Wiki | The GIS Encyclopedia Dead reckoning For other uses, see Dead reckoning (disambiguation) . The navigator plots his 9am position, indicated by the triangle, and, using his course and speed, estimates his position at 9:30am and 10am. Dead reckoning (DR) is the process of estimating one's current position based upon a previously determined position, or fix , and advancing that position based upon known or estimated speeds over elapsed time, and course. While traditional methods of dead reckoning are no longer considered primary means of navigation , modern inertial navigation systems , which also depend upon dead reckoning, are very widely used. A disadvantage of dead reckoning is that since new positions are calculated solely from previous positions, the errors of the process are cumulative, so the error in the position fix grows with time. Contents 9 External links Animal navigation In studies of animal navigation, dead reckoning is more commonly (though not exclusively) known as path integration , and animals use it to estimate their current location based on the movements they made since their last known location.

Animals such as ants, rodents, and geese have also been shown to continuously keep track of their locations relative to a starting point and return to it, an important skill to have for creatures that forage for food and then return to a fixed home. [1] Marine navigation In marine navigation a "dead" reckoning plot generally does not take into account the effect of currents or wind. Aboard ship a dead reckoning plot is considered important in evaluating position information and planning the movement of the vessel. [2] Dead reckoning begins with a known position, or fix , which is then advanced, mathematically or directly on the chart, by means of recorded heading, speed, and time. Speed can be determined by many methods. Before modern instrumentation, it was determined aboard ship using a chip log. More modern methods include pit log referencing engine speed (e.g. in rpm) against a table of total displacement (for ships) or referencing one's indicated airspeed fed by the pressure from a Pitot tube. This measurement is converted to an equivalent airspeed based upon known atmospheric conditions and measured errors in the indicated airspeed system.

A naval vessel uses a device called a pit sword (rodmeter), which uses two sensors on a metal rod to measure the electromagnetic variance caused by the ship moving through water. This change is then converted to ship's speed. Distance is determined by multiplying the speed and the time. This initial position can then be adjusted resulting in an estimated position by taking into account the current (known as set and drift in marine navigation). If there is no positional information available, a new dead reckoning plot may start from an estimated position. In this case subsequent dead reckoning positions will have taken into account estimated set and drift. Dead reckoning positions are calculated at predetermined intervals, and are maintained between fixes. The duration of the interval varies. Factors including one's speed made good and the nature of heading and other course changes, and the navigator's judgment determine when dead reckoning positions are calculated. Before the development of the marine chronometer, dead reckoning was the primary method of determining longitude available to mariners such as Christopher Columbus and John Cabot on their trans-Atlantic voyages. Tools such as the Traverse board were developed to enable even illiterate crew members collect the data needed for dead reckoning.

Air navigation Traditionally, in air navigation, displacement or position caused by wind were taken into account, using a tool called a wind triangle. Generally speaking, dead reckoning positions were calculated at least once every 300 miles and when making combined turns totaling more than 30 degrees from the initial heading out of the last DR position. Today, dead reckoning is rarely used in this traditional form for air navigation, but it survives in the form of inertial navigation systems , which are nearly universal on more advanced aircraft. The INS is used in combination with other navigation aids, such as GPS , in order to provide reliable navigation capability under virtually any conditions, with or without external navigation references. Automotive navigation Dead reckoning is today implemented in some high-end automotive navigation systems in order to overcome the limitations of GNSS technology alone. Satellite microwave signals are unavailable in parking garages and tunnels, and often severely degraded in urban canyons and near trees due to blocked lines of sight to the satellites or multipath propagation. In a dead-reckoning navigation system, the car is equipped with sensors that record the wheel rotation and steering direction.

These sensors are often already present in cars for other purposes (anti-lock braking system, electronic stability control) and can be read by the navigation system from the controller-area network bus. The navigation system then uses a Kalman filter in order to integrate the reliability and short-term accuracy of the sensor data with the long-term accuracy of the satellite data into a position fix that combines the best of both worlds. Etymology There is disagreement about the derivation of the phrase. It is sometimes thought (particularly among sailors and pilots in the USA [3] ) to come from deduced reckoning and is sometimes given in modern sources as an alternatively spelled ded reckoning; however, according to the Oxford English Dictionary, the phrase dead reckoning dates from Elizabethan times (1605–1615), and no trace of it can be found in books published before the 20th Century [4] . The popular etymology from deduced is not documented in the Oxford English Dictionary or any other historical dictionary. It is not clear what 'dead' might mean in the context of dead reckoning, and several alternative theories have been promulgated [5] .

Math Here are the dead reckoning formulas for the coordinates (x and y), and heading( ) for a differential drive robot with encoders on both drives: where are the encoder ticks recorded on drive one, are the encoder ticks recorded on drive two, is the radius of the drive wheel, and is the number of encoder ticks recorded in a full, in-place rotation. See also Attitude and Heading Reference Systems Celestial navigation Marine Chronometer | Longitude | Time The 17 th century was the age of travel and colonization. Many long sea voyages wereundertaken to different parts of the world. This period was known as the ‘Age of Discovery’. The ‘Age of Discovery’ or rather the ‘Age of Exploration’ began aroundthe 15h century and progressed all the way to the 18 th century. This was the age wheremany explorers from the British Empire and European Countries set sail to discover other parts of the world for trade. Most of these voyages spanned many months or years and were voyages over seas. Hence good navigation was necessary.

When theearly navigators started venturing away from the sight of land they started developingmethods of navigation involving the heavenly bodies.To determine a position on the earth's surface, it is necessary and sufficient to know both the latitude, longitude. Methods of determining the latitude existed during the17 th century however there were no good methods of determining the longitude.Determining latitude was relatively easy in that it could be found from the altitude of the sun at noon with the aid of a table giving the sun's declination for the day. For longitude, early ocean navigators had to rely on dead reckoning or Galileo's methodDead reckoning (DR) is the process of estimating one's current position based upon a previously determined position, or fix and advancing that position based upon knownor estimated speeds over elapsed time, and course. The disadvantage of deadreckoning was that since new positions were calculated solely from previous positions, the errors of the process were cumulative, so the error in the position fixgrew with time.

Hence dead reckoning was inaccurate on long voyages out of sight of land and these voyages sometimes ended in tragedy as a result.Galileo's method based on observing Jupiter's natural satellites, was usually not possible at sea due to the ship's constant motion.In order to avoid problems with not knowing one's position accurately, navigatorsused to, where possible, take advantage of their knowledge of latitude. They used tosail to the latitude of their destination, turn toward their destination and follow a lineof constant latitude. This was known as running down ‘a westing’ (if westbound,easting otherwise). This prevented a ship from taking the most direct route (a greatcircle) or a route with the most favorable winds and currents, extending the voyage bydays or even weeks. This increased the likelihood of short rations, scurvy or starvation leading to poor health or even death for members of the crew. Henceoverall this method was a risk to the ship.Errors in navigation had also resulted in shipwrecks. Most of those disasters wereattributed to serious errors in reckoning position at sea. One such example was theloss of Admiral Cloudesley Shovell and his fleet.

In 1707 Sir Cloudesley Shovell wasreturning from Gibraltar with his fleet when he sailed into cloudy weather. After 12days with no sight of land they calculated they were west of the southern tip of England and decided to hold station. That night hey ran ground on the Scilly Isleslosing 4 ships and nearly 2000 crew members including the Admiral.Hence an accurate method of determining the longitude had to be discovered. TheLongitude Board was introduced. The Board of Longitude was the popular name for the Commissioners for the Discovery of the Longitude at Sea.

It was a British1 Government body formed in 1714 to solve the problem of finding longitude at sea.The Board gathered the greatest scientific minds of its day to work on the problem,including Sir Isaac Newton, and also put up prizes for those who could demonstrate aworking device or method.The main longitude prizes were:£10,000 for a method that could determine longitude within 60 nautical miles (111km)£15,000 for a method that could determine longitude within 40 nautical miles (74 km)£20,000 for a method that could determine longitude within 30 nautical miles (56km).In addition, the Board had the discretion to make awards to persons who were makingsignificant contributions to the effort or to provide ongoing financial support to thosewho were working productively towards the solution. The Board could also makeadvances of up to £2,000 for experimental work deemed promising.It was during this time that John Harrison invented the marine chronometer. This wasan instrument for determining the longitude of the place.

Chronometer is a clock thatmeasures time with great accuracy and is used in navigation to help mariner (with thehelp of some astronomic tables) for determining its precise location on the water while they were in the middle of the ocean. Hence it was thanks to John Harrison’sdiscovery that safer voyages over seas could be made.A longitude describes the location of a place on Earth east or west of a north-southline called the Prime Meridian. Longitude is given as an angular measurement rangingfrom 0° at the Prime Meridian to +180° eastward and −180° westward. Manysolutions were proposed for how to determine longitude at the end of an exploratorysea voyage, and hence, the longitude of the place that was visited (in case, for instance, one would want to revisit the location or place it on a map). The practicalmethods relied on a comparison of local time with the time at a given place (such asGreenwich or Paris).Harrison instead set out to solve the problem in probably the most direct way: by producing a reliable clock. The theory was simple and had been first proposed byFrisius.

The difficulty, however, was in producing a clock which could maintainaccurate time on a lengthy, rough sea voyage with widely-varying conditions of temperature, pressure and humidity. Frisius had realized that to determine longitude, aclock would have to be “of great exactness”. Many leading scientists including Newton and Huygens doubted that such a clock could ever be built and had moreoptimism for astronomical observations (such as the Method of Lunar Distances).Huygens ran trials using both a pendulum and a spiral balance spring clock asmethods of determining longitude. Although both types showed some favorableresults, they were both prone to fickleness. Newton observed that “A good watch mayserve to keep a reckoning at sea for some days and to know the time of a celestialobservation; and for this end a good Jewel may suffice till a better sought of watchcan be found out. But when longitude at sea is lost, it cannot be found again by anywatch.” However, if such a clock were built and set at noon in London at the start of avoyage, it would subsequently always tell you how far from noon it was in London atthat second, regardless of where you had traveled.

By referring to the clock when it is2 noon locally (i.e. the Sun is at its highest in the sky where you are) you can read,almost directly from the clock face, how far around the world you are from London.For instance, if the clock shows that it is midnight in London when it is noon locally,then you are half way round the world, (e.g. 180 degrees of longitude) from London.After steadfastly pursuing various methods during thirty years of experimentation,Harrison finally designed and built the world's first successful marine chronometers,the highly accurate maritime time-keeping instruments that, for the first time, alloweda navigator to accurately assess his ship's position in longitude. This is so because theearth is constantly rotating, and therefore knowing the time whilst making an altitudemeasurement to a known heavenly body such as the sun, provided critical data for aship's position east-west—a necessary capability for re-approaching land after voyages over medium and long distances.Knowing such measurements without an accurate time could only show position inlatitude which was a trivial problem in comparison.

Such a maritime clock had to benot only highly accurate over long time intervals, but relatively impervious tocorrosion in salt air, able to tolerate wide variations in temperature and humidity andin general durable whilst able to function at the odd angles and pitch and yaw typicalof decks under strong waves and storm tossed conditions.Yet the timekeeping device with such accuracy would eventually also allow thedetermination of longitude accurately, making the device a fundamental key to themodern age. Nonetheless, for many years even after the American Revolution,chronometers were expensive rarities, as their adoption and use proceeded slowly dueto the precision manufacturing necessary and hence high expense, but by the early19th century, navigation at sea without one was considered unwise to unthinkable.Using a chronometer to aid navigation simply saved lives and ships—the insuranceindustry, exercise of self-interest, and common sense did the rest in making the devicea universal tool of maritime trade.3 More From This User

Question: In navigation, what is the process of estimating one's current position based upon a previously determined position and advancing it using estimated speed over elapsed time, and course?
Answer: Dead reckoning